Elliptic curve data - 6936.p1

Formats: - HTML - YAML - JSON - 2024-04-29T20:44:07.873352

• ec_curvedata •

  Column	Type
  Ciso	text
  Clabel	text
  Cnumber	smallint
  abc_quality	double precision
  absD	numeric
  adelic_genus	integer
  adelic_index	integer
  adelic_level	bigint
  ainvs	numeric[]
  analytic_rank	smallint
  bad_primes	integer[]
  class_deg	smallint
  class_size	smallint
  cm	smallint
  conductor	integer
  degree	bigint
  elladic_images	text[]
  faltings_height	numeric
  faltings_index	smallint
  faltings_ratio	smallint
  iso_nlabel	smallint
  isogeny_degrees	smallint[]
  jinv	numeric[]
  lmfdb_iso	text
  lmfdb_label	text
  lmfdb_number	smallint
  manin_constant	smallint
  min_quad_twist_ainvs	numeric[]
  min_quad_twist_disc	smallint
  modell_images	text[]
  modm_images	text[]
  nonmax_primes	smallint[]
  nonmax_rad	integer
  num_bad_primes	smallint
  num_int_pts	integer
  optimality	smallint
  potential_good_reduction	boolean
  rank	smallint
  regulator	numeric
  semistable	boolean
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '6936m', 'Clabel': '6936m5', 'Cnumber': 5, 'abc_quality': 1.2105879594055395, 'absD': 444903671808, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 816, 'ainvs': [0, 1, 0, -111072, -14285088], 'analytic_rank': 1, 'bad_primes': [2, 3, 17], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 6936, 'degree': 20480, 'elladic_images': ['16.48.0.210'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.4644015665081960768829887536', 'prec': 100}, 'faltings_index': 5, 'faltings_ratio': 8, 'iso_nlabel': 15, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [3065617154, 9], 'lmfdb_iso': '6936.p', 'lmfdb_label': '6936.p1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -384, -2772], 'min_quad_twist_disc': 17, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0.r.1', '16.48.0.l.1', '24.48.0.bf.1', '48.96.1.bv.1', '68.12.0-4.c.1.1', '136.48.0.?', '272.96.0.?', '408.96.0.?', '816.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '10.160108880036726843949084896', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.58759002103319516354090800001', 'prec': 107}, 'szpiro_ratio': 5.253831889264282, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
• ec_classdata •

  Column	Type
  anlist	smallint[]
  aplist	smallint[]
  class_deg	smallint
  class_size	smallint
  conductor	integer
  isogeny_matrix	smallint[]
  lmfdb_iso	text
  trace_hash	bigint

  
  {'anlist': [0, 1, 0, 1, 0, 2, 0, 0, 0, 1, 0, -4, 0, -2, 0, 2, 0, 0, 0, -4, 0], 'aplist': [0, 1, 2, 0, -4, -2, 0, -4, 8, -6, -8, -6, 6, 4, 0, -2, 4, 2, -4, -8, -10, 8, -4, -6, -2], 'class_deg': 8, 'class_size': 6, 'conductor': 6936, 'isogeny_matrix': [[1, 8, 2, 4, 8, 4], [8, 1, 4, 2, 4, 8], [2, 4, 1, 2, 4, 2], [4, 2, 2, 1, 2, 4], [8, 4, 4, 2, 1, 8], [4, 8, 2, 4, 8, 1]], 'lmfdb_iso': '6936.p', 'trace_hash': 814227522005024665}
• ec_mwbsd •

  Column	Type
  area	numeric
  conductor	integer
  gens	numeric[]
  heights	numeric[]
  lmfdb_label	text
  ngens	smallint
  rank_bounds	smallint[]
  real_period	numeric
  sha_an	numeric
  special_value	numeric
  tamagawa_product	integer
  torsion_generators	numeric[]
  xcoord_integral_points	numeric[]

  
  {'area': {'__RealLiteral__': 0, 'data': '0.053460985557815277655330784327', 'prec': 107}, 'conductor': 6936, 'gens': [[362369, 200702697, 20]], 'heights': [{'__RealLiteral__': 0, 'data': '10.160108880036726843949084896', 'prec': 100}], 'lmfdb_label': '6936.p1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.26151593523347914264892657517', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.3140607516735619309313291994149910308', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-193, 0, 1]], 'xcoord_integral_points': [-193]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [4, 0], '5': [3, 0], '7': [3, 1, 0], '11': [1, 0], '13': [1, 0], '17': 'a', '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [3, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '6936.p1'}
• ec_torsion_growth •

  Column	Type
  degree	smallint
  field	numeric[]
  lmfdb_label	text
  torsion	smallint[]

  
  
  • id: 365199
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '6936.p1', 'torsion': [2, 2]}
  • id: 365201
    {'degree': 2, 'field': [17, 0, 1], 'lmfdb_label': '6936.p1', 'torsion': [4]}
  • id: 365200
    {'degree': 2, 'field': [34, 0, 1], 'lmfdb_label': '6936.p1', 'torsion': [4]}
  • id: 365204
    {'degree': 4, 'field': [25, 0, 7, 0, 1], 'lmfdb_label': '6936.p1', 'torsion': [8]}
  • id: 365202
    {'degree': 4, 'field': [81, 0, 16, 0, 1], 'lmfdb_label': '6936.p1', 'torsion': [2, 4]}
  • id: 365203
    {'degree': 4, 'field': [529, 0, 22, 0, 1], 'lmfdb_label': '6936.p1', 'torsion': [8]}
  • id: 365205
    {'degree': 8, 'field': [-302, 1192, -1132, -104, 13, 44, -10, -4, 1], 'lmfdb_label': '6936.p1', 'torsion': [2, 4]}
  • id: 365206
    {'degree': 8, 'field': [358, 152, -52, -184, 53, 44, -10, -4, 1], 'lmfdb_label': '6936.p1', 'torsion': [8]}
  • id: 365207
    {'degree': 8, 'field': [1753, 948, 888, 168, 89, -12, 6, 0, 1], 'lmfdb_label': '6936.p1', 'torsion': [2, 8]}
  • id: 365208
    {'degree': 8, 'field': [2857, 1008, 956, 192, 105, -12, 2, 0, 1], 'lmfdb_label': '6936.p1', 'torsion': [16]}
  • id: 365209
    {'degree': 8, 'field': [6498, -11304, 4878, -1454, 320, -26, 4, -4, 1], 'lmfdb_label': '6936.p1', 'torsion': [6]}
  • id: 365214
    {'degree': 16, 'field': [-77032609, -81312488, 208649536, -159297944, 82471842, -31822400, 8680244, -1843360, 271680, -28576, 5584, -1376, 318, -56, 20, -8, 1], 'lmfdb_label': '6936.p1', 'torsion': [2, 6]}
  • id: 365211
    {'degree': 16, 'field': [16866, 46296, 54524, 72616, 70130, 44088, 62424, 8896, 28579, 88, 6528, -120, 762, -8, 44, 0, 1], 'lmfdb_label': '6936.p1', 'torsion': [2, 8]}
  • id: 365210
    {'degree': 16, 'field': [100258, 25688, -8524, -71592, 159290, -222416, 166912, -21384, -59117, 30648, 5416, -5320, 98, 336, -28, -8, 1], 'lmfdb_label': '6936.p1', 'torsion': [4, 4]}
  • id: 365216
    {'degree': 16, 'field': [431649, 1277208, 1316898, 673722, 50868, -131634, 134644, 5040, 67588, -11656, 10180, -454, 724, -34, 34, 0, 1], 'lmfdb_label': '6936.p1', 'torsion': [12]}
  • id: 365212
    {'degree': 16, 'field': [1020393, 8513208, 17063496, -2681424, 2186376, 899928, -2385864, -81504, 491062, -3768, -51496, 624, 3048, -24, -88, 0, 1], 'lmfdb_label': '6936.p1', 'torsion': [16]}
  • id: 365213
    {'degree': 16, 'field': [1992073, -1639516, 2267700, -1407764, 1107912, -559536, 320872, -135836, 62001, -22288, 8356, -2532, 786, -196, 48, -8, 1], 'lmfdb_label': '6936.p1', 'torsion': [2, 16]}
  • id: 365215
    {'degree': 16, 'field': [25522704, 0, 26876736, 0, 10945728, 0, 2522320, 0, 367544, 0, 34456, 0, 2020, 0, 68, 0, 1], 'lmfdb_label': '6936.p1', 'torsion': [12]}
• ec_localdata •

  Column	Type
  conductor	integer
  conductor_valuation	smallint
  discriminant_valuation	smallint
  j_denominator_valuation	smallint
  kodaira_symbol	smallint
  lmfdb_label	text
  prime	integer
  reduction_type	smallint
  root_number	smallint
  tamagawa_number	smallint

  
  
  • id: 141914
    {'conductor': 6936, 'conductor_valuation': 3, 'discriminant_valuation': 11, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '6936.p1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 141915
    {'conductor': 6936, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '6936.p1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 141916
    {'conductor': 6936, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '6936.p1', 'prime': 17, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 1709869
    {'adelic_gens': [[5, 4, 812, 813], [1, 16, 0, 1], [52, 85, 663, 562], [15, 2, 718, 803], [575, 0, 0, 815], [307, 544, 102, 613], [1, 0, 16, 1], [801, 16, 800, 17], [749, 544, 544, 69]], 'adelic_image': '816.192.1.?', 'conductor': 6936, 'lmfdb_label': '6936.p1', 'prime': 0}
  • id: 34334
    {'conductor': 6936, 'elladic_image': '16.48.0.210', 'lmfdb_label': '6936.p1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 279184
    {'lmfdb_iso': '6936.p', 'p': 5, 'prec': 20, 'unit': 1316569681442, 'val': 2}
  • id: 279192
    {'lmfdb_iso': '6936.p', 'p': 11, 'prec': 20, 'unit': 13388944104743379653, 'val': 1}
  • id: 279190
    {'lmfdb_iso': '6936.p', 'p': 13, 'prec': 20, 'unit': 1370654963062043649009, 'val': 1}
  • id: 279193
    {'lmfdb_iso': '6936.p', 'p': 19, 'prec': 20, 'unit': 341019950141491071655412, 'val': 1}
  • id: 279196
    {'lmfdb_iso': '6936.p', 'p': 23, 'prec': 20, 'unit': 61137464116940586579702755, 'val': 1}
  • id: 279189
    {'lmfdb_iso': '6936.p', 'p': 29, 'prec': 20, 'unit': 2120566852741237113440037000, 'val': 1}
  • id: 279186
    {'lmfdb_iso': '6936.p', 'p': 31, 'prec': 20, 'unit': 1431436370489554109052245426, 'val': 1}
  • id: 279200
    {'lmfdb_iso': '6936.p', 'p': 37, 'prec': 20, 'unit': 15722513191373051114251964784, 'val': 2}
  • id: 279187
    {'lmfdb_iso': '6936.p', 'p': 41, 'prec': 20, 'unit': 4140360272084198685888542343584, 'val': 1}
  • id: 279188
    {'lmfdb_iso': '6936.p', 'p': 43, 'prec': 20, 'unit': 8662389586090000120943413861646, 'val': 1}
  • id: 279194
    {'lmfdb_iso': '6936.p', 'p': 53, 'prec': 20, 'unit': 379630849765834550730214047825225, 'val': 1}
  • id: 279198
    {'lmfdb_iso': '6936.p', 'p': 59, 'prec': 20, 'unit': 4045803127939163432455137264626643, 'val': 1}
  • id: 279199
    {'lmfdb_iso': '6936.p', 'p': 61, 'prec': 20, 'unit': 4196921694483038245729373093488408, 'val': 1}
  • id: 279183
    {'lmfdb_iso': '6936.p', 'p': 67, 'prec': 20, 'unit': 1025739607261630425032647803562160, 'val': 1}
  • id: 279185
    {'lmfdb_iso': '6936.p', 'p': 71, 'prec': 20, 'unit': 68551492713222270710624276614512368, 'val': 1}
  • id: 279195
    {'lmfdb_iso': '6936.p', 'p': 73, 'prec': 20, 'unit': 218715342023497519346297506878897844, 'val': 1}
  • id: 279191
    {'lmfdb_iso': '6936.p', 'p': 79, 'prec': 20, 'unit': 1112676240166235557910270981555607445, 'val': 1}
  • id: 279182
    {'lmfdb_iso': '6936.p', 'p': 83, 'prec': 20, 'unit': 2708936446694177879024580480831640472, 'val': 1}
  • id: 279197
    {'lmfdb_iso': '6936.p', 'p': 89, 'prec': 20, 'unit': 6544932800126085138254507541694062621, 'val': 1}
  • id: 279181
    {'lmfdb_iso': '6936.p', 'p': 97, 'prec': 20, 'unit': 19861561096010544234689609247460618217, 'val': 1}